Claim 7.21 (Triangle inequality, adapted from [1]}) 
Let \(s \in \mathbb {N}^+\)  and \(\mathcal {T}\)  be an \(s\) -interval splitting tree. Then
\(\operatornamewithlimits{\mathbb {E}}_{w \in W[0,s-1]}{ \left\Vert {\mathbf {Z}_{w}} - \prod _{i=0}^{s-1}*{\mathbf {Z}_{w(i)}} \right\Vert _1} \le \sum _{(k_1,k_2,k_3)\in \mathcal {T}} ~\operatornamewithlimits{\mathbb {E}}_{w \in W[k_1,k_3]}{ \left\Vert {\mathbf {Z}_{w}} - *{\mathbf {Z}_{w(k_1,k_2)}}*{\mathbf {Z}_{w(k_2+1,k_3)}}  \right\Vert _1},\) 
